The 25-year-old has been limited to just seven starts for Real this season and it is believed that the France international is pushing for a move to Old Trafford.
To speed up a possible transfer, it is believed that Diarra will ask for a new contract before using the lack of a new deal to request a move.
And although Jose Mourinho has claimed he is not willing to sell the former Arsenal, Chelsea and Portsmouth player, an offer of £14m, £3m more than the Red Devils’ reported valuation, could convince him to do a deal.
Diarra joined Madrid from Portsmouth for £20m in January 2009 and has gone on to make 53 appearances in all competitions, scoring one goal.
Speaking last month, Diarra had insisted that he was keen to remain a Madridista, telling reporters: “I’m at Real Madrid and I have a contract. A month ago the situation was more difficult, but I hope to play here. Currently I am thinking only of the next game, but I don’t know if I will remain here.
“I am trying to enjoy my football without thinking about the future.”
